"What saves a man is to take a step.
Then another step." ~ C. S. Lewis

Sunday, December 30, 2007

Mathematical Challenges For the 21st Century

Benjamin Mann of DARPA has constructed a list of 23 challenges for mathematics for this century. Here are five of the top challenges:

1. The Mathematics of Quantum Computing, Algorithms, and Entanglement (DARPA 15) : “In the last century we learned how quantum phenomena shape our world. In the coming century we need to develop the mathematics required to control the quantum world.”

3. Geometric Langlands and Quantum Physics (DARPA 17) : “How does the Langlands program, which originated in number theory and representation theory, explain the fundamental symmetries of physics? And vice versa?”